Publication number | US7379508 B1 |

Publication type | Grant |

Application number | US 11/488,390 |

Publication date | May 27, 2008 |

Filing date | Jul 18, 2006 |

Priority date | Apr 9, 2001 |

Fee status | Paid |

Also published as | US7583748, US20080232505 |

Publication number | 11488390, 488390, US 7379508 B1, US 7379508B1, US-B1-7379508, US7379508 B1, US7379508B1 |

Inventors | Naofal Al-Dhahir |

Original Assignee | At&T Corp. |

Export Citation | BiBTeX, EndNote, RefMan |

Patent Citations (14), Non-Patent Citations (4), Referenced by (2), Classifications (7), Legal Events (2) | |

External Links: USPTO, USPTO Assignment, Espacenet | |

US 7379508 B1

Abstract

Space-time block coding is combined with single-carrier, minimum-mean-square-error, frequency-domain equalization for wireless communication through a medium characterized by multi-paths. The transmitter encodes incoming symbols into two or more streams that are transmitted over a corresponding number of transmitting antennas. The encoding employs modulo arithmetic. Decoding in the receiver proceeds by converting received signals to frequency domain, linearly combining the signals to separate contribution of the signals from the two or more transmitting antennas equalizing the separated signals, converting the equalized signals to time domain, and applying the converted signals to a decision circuit.

Claims(1)

an encoder responsive to blocks of incoming symbols, each block containing N of said incoming symbols, and encoding said N blocks of incoming symbols into two streams of symbols in pairs of output frames k and k+1, yielding output frame pairs x_{1} ^{k}, x_{1} ^{k+1}, and x_{2} ^{k}, x_{2} ^{k+1}, where each of a the frames includes v prefix symbols, each being applied to a different one of said two antennas, where x_{1} ^{k+1}(n)=− x _{2} ^{k}((n)_{N}) and x_{2} ^{k+1}(n)= x _{1} ^{k}((n)_{N}) and (•)_{N }denoted modulo N operation.

Description

This application is a continuation of application Ser. No. 11/231,451 filed Sep. 21, 2005 now U.S. Pat. No. 7,173,976, which is a continuation of application Ser. No. 10/026,148, filed Dec. 19, 2001 now U.S. Pat. No. 7,092,450. This application is also related to Provisional Application 60/282,634, filed Apr. 9, 2001.

This relates to space-time coding, and more particularly, to frequency domain equalization in a receiver that receives signals from a multi-path channel.

M. V. Clark, in “Adaptive Frequency-Domain Equalization and Diversity Combining for Broadband Wireless Communications,” *IEEE Journal on Selected Areas in Communications*, pp. 1385-1395, October 1998, has shown that single-carrier minimum-mean-square-error frequency-domain (SC MMSE FDE) is an attractive equalization scheme for broadband wireless channels that are characterized by their long impulse response memories. Primarily the advantage of this approach accrues from using the computationally efficient Fast Fourier Transform (FFT), which compares favorably with time-domain equalization, where complexity grows exponentially with channel memory or require very long FIR filters to achieve acceptable performance. Further more, H. Sari et al, in “Transmission Techniques for Digital Terrestrial TV Broadcasting,” *IEEE Communications Magazine*, pp 100-190, February 1995, have shown that SC MMSE FDE has two main advantages over Orthogonal Frequency Division Multiplexing (OFDM); namely, lower peak-to-average ration, and reduced sensitivity to carrier frequency errors.

Diversity transmission using space-time block coding, for example, like disclosed in U.S. Pat. No. 6,185,258, has been proposed for several wireless standards because of the many attractive features of such coding. The SC MMSE FDE was combined with receive diversity by G. Kadel, in “Diversity and Equalization in Frequency Domain—A Robust and Flexible Receiver Technology for Broadband Mobile Communications Systems,” *VTC*, pp. 894-898, May 1997. There has also been some recent work on combining the scheme disclosed in the U.S. Pat. No. 6,185,258 patent with OFDM, as reported by Liu et al in “Decoding and Equalization of Unknown Multipath Channels Based on Block Precoding and Transmit-Antenna Diversity,” *Asilomar Conf. On Signals, Systems, and Computers*, pp. 1557-1561, 1999. However, it has not been realized that various communication advantages result from combining space-time block coding with SC MMSE FDE.

An advance in the art is achieved by combining space-time block coding in a transmitter, for example, of a mobile unit, with SC MMSE FDE in a responsive receiver, for example in a base station. Illustratively, in a two transmitting antenna arrangement, the transmitter handles two blocks of N incoming symbols x_{a}(n) and x_{b}(n) at a time, encodes the block of N symbols into two streams, and transmits the two streams over two separate antennas in two consecutive frames, k, and k+1. In frame k, one antenna transmits symbols x_{1} ^{k}(n), while the other antenna transmits symbols x_{2} ^{k}(n). Symbols x_{1} ^{k}(n) can, for example, equal symbols x_{a}(n), while symbols x_{2} ^{k}(n) can equal x_{b}(n). In frame k+1, the one antenna transmits symbols x_{1} ^{k+1}(n), while the other antenna transmits symbols x_{2} ^{k+2}(n). The relationships adopted for x_{1} ^{k+1}(n) and x_{2} ^{k+2}(n) are x_{1} ^{k+1}(n)=− _{2} ^{k}((−n)_{N}) and x_{2} ^{k+1}(n)= _{1} ^{k}((−n)_{N}) where _{2} ^{k }is the complex conjugate of _{2} ^{k}. At the receiver, the received signal is transformed into the frequency domain, processed, equalized, transformed to time domain, and applied to a slicer to recover the transmitted sequences x_{1} ^{k}(n) and x_{2} ^{k}(n).

More specifically, the processing within the receiver multiplies Y, (which is the received signal that is transformed into the frequency domain) by Λ*. The matrix Λ* is the complex conjugate of Λ, where

Λ_{1 }is a diagonal matrix with elements (q,q) that are equal to the q^{th }DFT coefficient of the transfer function between the one transmitting antenna and the receiver, and Λ_{2 }is a diagonal matrix with elements (q,q) that are equal to the q^{th }DFT coefficient of the transfer function between the other transmitting antenna and the receiver. Signal Y comprises signal Y^{k }for frame k, and signal Y^{k+1 }for frame k+1. The frequency domain equalization is effected through multiplication of the signals forming vectors Y^{k }and Y^{k+1 }by a diagonal matrix whose elements are related to the DFT coefficients between the one transmitting antenna and the receiver, and the other transmitting antenna and the receiver.

Extension of the principles disclosed herein to arrangements where several transmitting unit concurrently operate on the same carrier frequency is also disclosed.

**15** of

The following mathematical development focuses on a system having two transmit antennas and one receive antenna. It should be understood, however, that a skilled artisan could easily extend this mathematical development to more than two transmit antennas, and to more than one receive antenna.

**11** and **12**, a receiver **20** with antenna **21**, and a transmission channel therebetween that has a memory of v symbols periods. The transmission channel between antennas **11** and **21** can be represented as a finite impulse response filter with v+1 taps having values h_{1}(**0**), h_{1}(**1**), . . . h_{1}(v), forming vector h_{1}. Similarly the channel between antennas **12** and **21** can be represented by h_{2}. Within transmitter **10**, encoder **15** outputs symbol blocks k=1, 2, 3, . . . , of two length N sequences; with one sequence, x_{1} ^{k}(n), n=0, 1, 2, . . . N−1, being transmitted by antenna **11**, and the other sequence, x_{2} ^{k}(n), n=0, 1, 2, . . . N−1, being transmitted by antenna **12**. In vector notation, the sequences can be expressed by x_{1} ^{k }and x_{2} ^{k}, respectively. Because the transmission channel between transmitter **10** and receiver **20** has memory of v symbols, absent any protection, a receiver will comingle receptions from adjacent blocks. To avoid this, transmitter **10** includes a control signal that causes encoder **15** to precede each block with a string of v prefix symbols. In accordance with the principles disclosed herein, the symbols are selected to create a circulant transfer matrix between transmitter (for example, of a mobile unit) **10** and receiver to (for example, of a base station), as shown below.

It was discovered that advantageous results accrue from encoder **15** generating sequences such that the blocks of generated sequences are generated in pairs, k and k+1, where

*x* _{1} ^{k+1}(*n*)=−* x *

for n=0, 1, . . . N−1 and k=0, 2, 4, . . . , where

{x(0),x(1),x(2), . . . x(N−2)x(N−1)},

for antenna

{

for antenna

and 0≦p, q≦N−1, is it follows that

*X* _{1} ^{k+1}(*m*)=−* X *

As will become clear from the disclosure below, the relationship of equation (2) allows for frequency domain decoupling in a receiver the contributions of sequences x_{1} ^{k}(n) and x_{2} ^{k}(n). Accordingly, for purposes of this disclosure, such encoding—the encoding of equation (1) being one example thereof, is termed “frequency domain decouplable contributions” (FD-DC) encoding. It is encompassed by a class of orthogonal designs, as disclosed, for example, in U.S. Pat. No. 6,088,408, issued Jul. 11, 2000

**15** delivers to antenna **11**, with the prefix string consisting symbols x_{1}(−v) through x_{1}(−1), followed by symbols x_{1}(**0**) through x_{1}(N−1). Ignoring the subscript, the signals received at antenna **21** in response to signals transmitted by antenna **11**, starting with signal y(**0**), which corresponds to the received signal at the time the encoded signal x(**0**) is transmitted by antenna **11**, can be expressed by the following matrix equation:

If the prefix sequence is chosen so that x(−i)=x(N−i) for i=1, 2, . . . v, then equation (3) can be replaced by

Returning to the use of subscripts to indicate the transmitting antenna, and superscripts to indicate symbol blocks, and recognizing that antenna **21** receives signals transmitted by antenna **12** as well as by antenna **11**, we get

*y* ^{k} *=H* _{1} *x* _{1} ^{k} *+H* _{2} *x* _{2} ^{k} *+n* ^{k} (5)

where

and the number of rows and columns in H_{a }is N.

A matrix with the structure of H_{a }is known as a circulant matrix, and it can be shown to have the eigen-decomposition

H_{a}=Q^{−1}Λ_{a}Q (7)

where (.)* denotes complex-conjugate transpose, Q^{−1 }is the inverse DFT matrix, and Λ_{a }is a diagonal matrix whose (q,q) element is equal to the q^{th }DFT coefficient of h_{a}. It may be noted that Q^{−1}=Q* which, of course simplifies processing since it is not necessary to compute the inverse of the matrix, and it is assumed that the characteristics of the transmission medium between transmitter **10** and receiver **20** are knows by means of any one of knows processes. See, for example, U.S. patent application Ser. No. 09/956,648 filed Sep. 20, 2001 by the inventor of this application. Accordingly, it is presumed that the DFT coefficients of h_{a }are known and, therefore, Λ_{a }is known.

It may be noted also that the above assumes that the transmission channel between transmitter **10** and receiver **20** does not change during the course of computations that are relevant to this disclosure, which is the time of two consecutive blocks.

Applying the output signals of circuit **22** to FFT circuit **23** to transform the signals of equations (5) into the frequency domain yields

and

*Y* ^{k+1}=Λ_{1} *X* _{1} ^{k+1}+Λ_{2} *X* _{2} ^{k+1} *+N* ^{k}. (9)

By taking advantage of the particular encoding by encoder **15**, as expressed in equation (2), one can note that equation (9) can be rewritten and expressed together with equation (8) by

*Y=ΛX+N. *

Noting that Λ is an orthogonal matrix, the two signals X_{1} ^{k }and X_{2} *k *can be decoupled by simply multiplying both sides of equation (10) by Λ*, resulting in

Expressed more succinctly,

from which we get

*{tilde over (Y)}* ^{k} *={tilde over (Λ)}X* _{1} ^{k} *+Ñ* ^{k }

*{tilde over (Y)}* ^{k+1} *={tilde over (Λ)}X* _{2} ^{k} *+Ñ* ^{k+1} (13)

where {tilde over (Λ)}=(Λ_{1}Λ_{1}*+Λ_{2}Λ_{2}*) in an N×N diagonal matrix.

Signals {tilde over (Y)}^{k+1 }and {tilde over (Y)}^{k }are computed in circuit **24** from

which corresponds to

*{tilde over (Y)}* ^{k+1}=Λ_{2} **Y* ^{k}+Λ_{2} * Y *

and

where signal Y

In accord with the principles disclosed herein, for the type transmitter structure disclosed above, a single-carrier minimum-mean-square-error frequency-domain equalization (SC-MMSE-FDE) is obtained with an N×N diagonal matrix applied to the signals of equations (15) and (16), where the elements of this matrix are given by

where

under the assumption that both the noise and the signal are “white.” It is noted that the noise vector n and its DFT N have the same variance, since the are related through the orthonormal transformation, Q.

Applying the output signals obtained by combiner **24** to SC-MMSE-FDE circuit **25**, wherein the matrix of equation (17) pre-multiplies the signals of equations (15) and (16), results in

where W{tilde over (Λ)} is a diagonal N×N matrix with elements

and

*Z* ^{k+1} *=W{tilde over (Λ)}X* _{1} ^{k+1} *+WÑ* ^{k+1} (19)

Applying equation (18) and equation (19) signals of circuit **25** to inverse FFT transform circuit **26** yields

and

*z* ^{k+1} *={tilde over (H)}x* _{2} ^{k} *+ñ,* (21)

where {tilde over (H)}=Q*W{tilde over (Λ)}Q has the same form as H in equation (7). Note that since the noise statistics are the same in frames k and k+1, equations (20) and (21) replace both Q*WQñ^{k }and Q*WQñ^{k+1 }with ii. Also note the {tilde over (H)} approaches the identity matrix as the value of SNR increases. For this reason,

Thus, the signals developed by circuit **26** correspond to the signals x_{1} ^{k }and x_{2} ^{k }that are filtered and equalized by matrix {tilde over (H)}, and augmented by noise. It is noted that the matrix {tilde over (H)} approaches the identity matrix as the value of SNR increases. For this reason a simple “slicer” detector can be used to detect the signals x_{1} ^{k }and x_{2} *k. *

Accordingly, the signals developed by circuit **26** are applied to detector **27**, which is a conventional slicer, yielding the signals x_{1} ^{k }and x_{2} ^{k}, from which the sequence of transmitted symbols is obtained.

Expanding on the principles disclosed herein, **20**, which has M antennas (two shown). Corresponding to such an arrangement, equation (10) is rewritten as

where Y_{21 }represents the signals received at antenna **21**, X_{10 }represents signals transmitted by unit **10**, Λ_{10−21 }represents the channel between unit **10** and antenna **21**, X_{30 }represents signals transmitted by unit **30**, Λ_{30−21 }represents the channel between unit **30** and antenna **21**, and N_{21 }is the noise received at antenna **21**. Similarly, Y_{22 }represents the signals received at antenna **22**, Λ_{30−22 }represents the channel between unit **30** and antenna **22**, Λ_{10−22 }represents the channel between unit **10** and antenna **22**, and N_{22 }is the noise received at antenna **22**.

The signals of the two units can be decoupled in each frame by applying the following linear, zero-forcing interference cancellation:

where {tilde over (Λ)}_{10−21}=Λ_{10−21}−Λ_{30−21}Λ_{30−22} ^{−1}Λ_{10−22 }and {tilde over (Λ)}_{10−22}=Λ_{30−22}−Λ_{10−22}Λ_{10−21} ^{−1}Λ_{30−21}. The critical observation to make here is that both {tilde over (Λ)}_{10−21 }and {tilde over (Λ)}_{10−22 }are orthogonal matrices like matrix Λ in equation (10) and, therefore, decoding proceeds as described above for the single unit case, and the full diversity gain is guaranteed for both users. That is, combiner **28** in **24** in

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Referenced by

Citing Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US7583748 * | May 27, 2008 | Sep 1, 2009 | Naofal Al-Dhahir | Frequency-domain method for joint equalization and decoding of space-time block codes |

US20080232505 * | May 27, 2008 | Sep 25, 2008 | Naofal Al-Dhahir | Frequency-domain method for joint equalization and decoding of space-time block codes |

Classifications

U.S. Classification | 375/267, 375/260 |

International Classification | H04B7/02 |

Cooperative Classification | H04B7/0854, H04B7/0669 |

European Classification | H04B7/08C4J2, H04B7/06C2C |

Legal Events

Date | Code | Event | Description |
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Sep 23, 2011 | FPAY | Fee payment | Year of fee payment: 4 |

Oct 27, 2015 | FPAY | Fee payment | Year of fee payment: 8 |

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